84. The Divisibility of Motion and Time

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Lecture Notes

Main Topics #

Two Ways Motion is Divisible #

• By the parts of the moving thing: When a thing with divisible parts is moved, the motion of the whole is composed of the motions of its parts. If the whole (AB) is moved, and AB consists of parts (AC and BC), then each part undergoes motion, and the whole motion equals the sum of the parts’ motions.
• By time: Since every motion occurs in time, and time is divisible, motion must be divisible in the same way. The divisions of time and motion necessarily correspond.

The Fundamental Role of the Moving Subject #

• The thing that moves is the basis for understanding divisibility in motion
• If the moving thing were indivisible (like a point), motion could not be divisible
• The moving subject’s divisibility is logically prior to understanding how motion itself is divisible

Proportion Between Motion, Time, and the Moving Thing #

• The divisibility of motion corresponds proportionally to the divisibility of time
• If motion is divisible into parts, then time is divisible into corresponding parts
• “The whole motion is in the whole [time], the half [motion] is in the half [time], the less in the less”
• This proportional relationship holds in all cases of divisible motion

Key Arguments #

Argument for Motion’s Divisibility by Parts #

1. Suppose AB is a body that moves, composed of divisible parts AC and BC
2. Each part AC and BC is moved (since the whole moves)
3. The motion of the whole must be composed of (or equal to) the motions of its parts
4. Therefore, motion is divisible according to the divisibility of the moving thing’s parts

Argument for Motion’s Divisibility by Time #

1. Every motion occurs in time
2. Time is divisible (into past, present, future; or into lesser periods)
3. Therefore, motion must be divisible in the same way as time is divisible
4. The divisions of time and motion are necessarily the same

The Proportionality Principle #

• If a body moves distance AB in time CD, then half the body moves half the distance in half the time
• This holds universally: less motion corresponds to less time, greater motion to greater time
• The proportion is exact and necessary

Important Definitions #

Motion (Motus) #

• The process occurring in time that is divisible in two corresponding ways
• Always involves something moving, time in which it moves, and extension of space/quality being traversed

Examples & Illustrations #

Body Moving Through Space #

• A body AB composed of parts AC and BC
• When the whole body moves, both parts move
• The total motion equals the sum of the motions of its parts
• Demonstrates divisibility by the moving subject’s parts

Temporal Division #

• A motion taking one and a half hours
• The motion’s divisibility mirrors time’s divisibility
• Half the motion takes half the time; a portion of the motion takes a portion of the time
• Shows the necessary correspondence between motion and time divisions

Questions Addressed #

In what ways is motion divisible? #

• Motion is divisible in two ways: by the divisibility of the moving thing and by the divisibility of time. These two modes of divisibility necessarily correspond to each other.

Why is the divisibility of the moving subject fundamental? #

• Because if the moving thing were not divisible (were a point or indivisible), motion could not be divisible. The moving thing’s divisibility grounds the possibility of divisible motion.

How do time and motion relate in their divisibility? #

• They are necessarily proportional. Every division of time corresponds to a division of motion, and vice versa. The divisions are the same in structure and measure.